The main reason that the leading strand is synthesized continuously while the lagging strand is synthesized in Okazaki fragments is due to the directionality of DNA synthesis. DNA polymerases can only synthesize new DNA in the 5' to 3' direction.
During DNA replication, the two strands of the double helix separate, creating a replication fork. The leading strand is oriented such that it can be synthesized continuously in the same direction as the replication fork is opening. Thus, DNA polymerase can add nucleotides continuously as it follows the unwinding of the helix.
On the other hand, the lagging strand is oriented in the opposite direction (3' to 5' relative to the fork) which means that as the fork opens, DNA polymerase cannot continuously synthesize in that direction. Instead, it must synthesize short segments of DNA (the Okazaki fragments) away from the replication fork, and then once a fragment is complete, the replication fork continues to open up new template DNA for additional fragments to be synthesized.
In summary, the synthesis on the leading strand is continuous because it aligns with the direction of the replication fork, while the lagging strand is synthesized in short fragments that must be pieced together later (due to the fact that DNA polymerase can only synthesize in the 5' to 3' direction). So, the correct statement would be:
DNA synthesis can take place only in the 5' to 3' direction.